No, it isn't. Imagine a hypothetical sterile human that was single celled - suddenly we've reached the same conclusion without the sub-organism reproduction issue. Making reproduction a core premise of being alive really drives to the idea of mortality, as reproduction is a way of overcoming our mortal coils. Yet, it is truly reasonable to classify reproduction as the only way? It also assumes a lineage, which is not required for synthetically created organisms.
I've said this elsewhere, but proteins are not required, in any regard, for life. They are an emergent phenomenon of the Earth's chemistry, not a rule for life. I mean, what is a cell even - "A fluid filled, membrane enclosed thing"? The reason cells are structured as they are is because of water, so a non-water based organisms would likely look much, much different.